Higher order volume and surface integral equation modeling of 3-D scattering and radiation problems

The method of moments (MoM), as one of the most powerful and versatile general numerical tools for electromagnetic-field computations based on discretizing integral equations in electromagnetics, has been especially effectively used for full-wave three-dimensional (3-D) solutions to open-region (e.g., scattering and radiation) problems in the frequency domain. In the MoM analysis in conjunction with the volume integral equation (VIE) approach, the volume equivalence principle is invoked to represent a scattering or radiation structure containing linear dielectric materials of arbitrary inhomogeneity and complexity by a distribution of volume electric (polarization and conduction) currents (the real currents) radiating in free space, and the resulting VIE, with the total volume current density vector, or another vector proportional to it, as unknown quantity, is discretized by the MoM. The analysis of composite dielectric and metallic radiation/scattering structures can be performed combining the VIE for dielectric parts and the surface integral equation (SIE) based on the boundary condition for the electric field intensity vector for metallic parts, with surface electric currents (again, the actual currents) treated as an unknown quantity. This gives rise to a hybrid VIE-SIE or VSIE formulation, which solves simultaneously for the volume currents throughout the dielectric domains and the surface currents over the metallic surfaces.